Remote sensing image classification by non-parallel SVMs

In the recent years, new techniques so called non-parallel support vector machines (NSVM) have been developed and applied to some synthetic and UCI machine learning data sets, yielding competitive results especially in terms of computational complexity and classification performance compared to classical SVM [1]. In binary classification task, the aim of NSVM is to find two non parallel hyperplanes such that each plane is as close as possible to one of the two classes and also as far as possible from the other class. The study of NSVM algorithms was first began with proximal SVM classification which generates two parallel hyperplanes [2]. Afterwards, it has been demonstrated by several different approaches that classification problems could also be tackled with the use of non-parallel hyperplanes. The first non-parallel hyperplane classifier was introduced by Mangarisan and Wild (2006) named as the generalized eigenvalue proximal support vector machine (GEPSVM) [3]. They removed/dropped the parallelism condition of the generated planes and make the first plane be located as close as possible to one data set while keeping it furthest from the points of the other data set and vice versa. Each proximal plane was found by solving two generalized eigenvalue problems instead of solving a quadratic programming problem as it was required for classical Support Vector Machine. In some cases, better classification accuracy results were achieved with GEPSVM in a short span of time compared to classical support vector machine classification algorithms [4].